In a large skillet over medium-high heat, brown the chicken in the vegetable oil. Turn each thigh to brown on both sides. Remove browned chicken from pan to a slow cooker (of at least 3 1/2-quart capacity). Deglaze pan by pouring in the wine, stirring and scraping to dissolve all cooked-on bits of food. Scrape this sauce into slow cooker. Add the mushrooms, onion, garlic, broth, tomato paste, basil, sugar, salt and pepper.

Cover and cook on LOW for 7 to 8 hours or on HIGH for 3 1/2 to 4 hours, just until chicken is very tender. Serve by spooning chicken over the cooked pasta, passing the Parmesan.